Heat the olive oil in a large Dutch oven or soup pot over medium heat. Add the sliced kielbasa and cook for 4–5 minutes, turning occasionally, until lightly browned; transfer it to a plate if the pot becomes crowded.

Add the diced onion, carrots, and celery to the same pot. Cook for 5–7 minutes, stirring occasionally, until the vegetables begin to soften and pick up the savory browned bits from the sausage.

Stir in the minced garlic, dried thyme, smoked paprika, kosher salt, and black pepper. Cook for about 30 seconds, just until the garlic is fragrant.

Pour in the chicken broth and diced tomatoes with their juices. Stir in the drained beans and browned kielbasa, scraping the bottom of the pot to loosen any flavorful bits.

Bring the soup to a boil, then reduce the heat and simmer uncovered for 15–20 minutes. Continue cooking until the carrots and celery are tender and the broth tastes savory and well blended.

Stir in the chopped kale and simmer for 4–6 minutes, until it is wilted and tender but still a lively green. Taste the soup and adjust the salt and pepper carefully.

Add the lemon juice or red wine vinegar if desired, stirring it through just before serving. Ladle the hot soup into bowls and serve immediately with crusty bread.